There are concepts that you can imagine - or at least think you can imagine - which aren't logically possible.
You can imagine or you can't. I'm not talking about can't.
If you can, then it's a logical possibility.
Can you imagine squaring the circle? Lots of mathematicians thought they could until it was proven to be impossible.
No they never imagined a square circle.
Some people
believed a square circle might be possible. They even have spent their whole like trying to prove their belief true. But not once did they imagine a square circle.
Can you imagine a program that always perfectly predicts whether a given program will halt on a given input? Probably you do think you can imagine that, but it's not logically possible, as Turing proved.
You see I stopped at "perfectly". I can't imagine "perfectly". Looking at the rest, well, no. I did a lot of programmation for my job and I know you don't imagine a programme. You write it. Same for all complex tasks. Management, military operations, sending men on the Moon.
Still, some people will do the hard job of imagining complex things. If they do that, then it's logically possibly. However, what is logically possible is exactly what they imagined, not necessarily what they say they have imagined. And most of the time, what people imagine is not realistic and never get to be realised. In effect, what people imagine is usually not realisable in practice. But, it will still be logically possible.
Can you imagine an anti-virus program that repels every computer virus? That's also impossible! (I doubt that Wikipedia has an entry for this, but there is a proof in my computer security textbook.)
You can't imagine that realistically. I don't think anyone sane would believe they can but that would be irrelevant. You can't imagine it. Whatever anyone did imagine was logically possible, though. But, what they imagine wouldn't be realisable. It wouldn't work.
Can you imagine a set of all sets that don't include themselves? Probably so, but it's not logically possible for such a set to exist.
Probably so? Whoa. No. Definitely not.
Whatever mathematician may have imagined it wasn't the set of all sets that don't include themselves. They imagined something, but not the set itself.
Can you imagine a consistent geometry that doesn't obey Euclid's axioms? Nobody could until non-Euclidean geometry was discovered.
So what? How does that falsify my claim? You're being illogical here.
For your information, at 14 I invented form scratch a new type of perspective similar to that of the fish-eye, before I saw my first fish-eye photo. I imagined it, and not only was it logically possible but it turned out to be actual.
And so you failed to mention that when non-Euclidean geometry was first proposed, people still though it couldn't exist. It's only with General Relativity that it became clear that not only was it a logical possibility but there was a probability that it was actual.
This is also very subjective. You say you cannot imagine God, but plenty of people think they can. Whose imagination is the standard for logical possibility?
People don't imagine God. They imagine something they call God. So, again, whatever people imagine, assuming their brain works well, it is logically possible. Still, where would be the problem with imagining that God exists? How would that be a counterexample to my thesis?
EB
